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Volume 7, Issue 4
A Convergence Analysis of the MINRES Method for Some Hermitian Indefinite Systems

Ze-Jia Xie, Xiao-Qing Jin & Zhi Zhao

DOI: 10.4208/eajam.181016.300517h

East Asian J. Appl. Math., 7 (2017), pp. 827-836.

Published online: 2018-02

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  • Abstract

Some convergence bounds of the minimal residual (MINRES) method are studied when the method is applied for solving Hermitian indefinite linear systems. The matrices of these linear systems are supposed to have some properties so that their spectra are all clustered around ±1. New convergence bounds depending on the spectrum of the coefficient matrix are presented. Some numerical experiments are shown to demonstrate our theoretical results.

  • Keywords

MINRES, Convergence bound, Hermitian indefinite, Toeplitz system.

  • AMS Subject Headings

65F10, 65F15, 65L05, 65N22

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-7-827, author = {Ze-Jia Xie, Xiao-Qing Jin and Zhi Zhao}, title = {A Convergence Analysis of the MINRES Method for Some Hermitian Indefinite Systems}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {7}, number = {4}, pages = {827--836}, abstract = {

Some convergence bounds of the minimal residual (MINRES) method are studied when the method is applied for solving Hermitian indefinite linear systems. The matrices of these linear systems are supposed to have some properties so that their spectra are all clustered around ±1. New convergence bounds depending on the spectrum of the coefficient matrix are presented. Some numerical experiments are shown to demonstrate our theoretical results.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.181016.300517h}, url = {http://global-sci.org/intro/article_detail/eajam/10723.html} }
TY - JOUR T1 - A Convergence Analysis of the MINRES Method for Some Hermitian Indefinite Systems AU - Ze-Jia Xie, Xiao-Qing Jin & Zhi Zhao JO - East Asian Journal on Applied Mathematics VL - 4 SP - 827 EP - 836 PY - 2018 DA - 2018/02 SN - 7 DO - http://doi.org/10.4208/eajam.181016.300517h UR - https://global-sci.org/intro/article_detail/eajam/10723.html KW - MINRES, Convergence bound, Hermitian indefinite, Toeplitz system. AB -

Some convergence bounds of the minimal residual (MINRES) method are studied when the method is applied for solving Hermitian indefinite linear systems. The matrices of these linear systems are supposed to have some properties so that their spectra are all clustered around ±1. New convergence bounds depending on the spectrum of the coefficient matrix are presented. Some numerical experiments are shown to demonstrate our theoretical results.

Ze-Jia Xie, Xiao-Qing Jin and Zhi Zhao. (2018). A Convergence Analysis of the MINRES Method for Some Hermitian Indefinite Systems. East Asian Journal on Applied Mathematics. 7 (4). 827-836. doi:10.4208/eajam.181016.300517h
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